What to do when you have too many vowels (other than panic)

This is the natural complement to the post about what to do when you have too many consonants. As mentioned before, if you dump one of your vowels, assuming that you are picking from the 144-letter Bananagrams distribution, you have an 8% chance of getting three vowels back. In my experience, if you have one extra vowel tile, and you just can't rearrange the grid to fit it in somewhere, even exchanging it for two vowels and a consonant tends to be easier to deal with. Of course, you could wind up with some consonants that are tricky to use (which may be why I rarely dump letters.. I also enjoy rearranging the grid).

Whatever approach you choose, you definitely want to know some words with a large percentage of vowels. There are some nice all-vowel words out there like aye, eye, and you. Here is a sampling of some longer vowel-heavy words:

eunoia (83% vowels)
eerie, adieu, audio, bayou (80%)
year, ooze, area, iota, auto (75%)
sequoia (71%)

"Eunoia" and "sequoia" are also distinctive for being two of the shortest word containing all five vowels. "Eunoia" may get you in trouble if you try to use it since it's an obscure word. [I am partial to it because it is a brain word. It comes from a Greek word meaning "beautiful/favorable thinking". The "beautiful thinking" interpretation led to the obscure English usage of "eunoia" - a state of normal mental health. A stricter reading suggests that the Greek word referred to thinking that was favorable to someone (like one's spouse). The "blissful and benevolent state of mind" interpretation, though questionable, is the nicest.]

If you are interested in obscure words on the extremes of human language, check out the All-Vowel Words and All-Consonant Words dictionaries. They start with tame words like "eau" and "brr" and then spin off into highly arcane references (at times approaching Borges-level bizarreness). They come packaged together in a book called "Wye's Dictionary of Improbable Words", downloadable from Lulu for ~$14 or buyable from Amazon for $25.

Pangrams and what to do when you have too many consonants

Pangrams are sentences that use every letter in the alphabet at least once. Just a few examples:

• Nth quark biz gyps cwm fjeld vox. (which sounds like the shortest science fiction story ever)
• Vext cwm fly zing jabs Kurd qoph.
  which I like for the description:
  "An annoyed fly in a valley, humming shrilly, pokes at the nineteenth letter of the Hebrew alphabet that was drawn by a Kurd." (though I prefer the variation: Zing! Vext cwm fly jabs Kurd qoph.)
• Squdgy fez, blank jimp crwth vox! (Translation: An imperative sentence, commanding one's squashed-down brimless hat to mute the skimpy voice of a Celtic violin. I like this one particularly, as it was made by my current hero, Claude Shannon, whom I will write about eventually, elsewhere.)

There are many more 26-letter pangrams. By adding two letters, one can make parsable pangrammatic sentences like:

• Waltz, bad nymph, for quick jigs vex!

As pointed out by Robert Munafo: "The fact that so many optimal pangrams exist in English results mainly from its highly complex and flexible grammar, and the borrowing of so many words from other languages."

In particular, all of the 26-letter pangrams above use Welsh words (which have made their way into the English language), since in Welsh, the letter W is a semivowel. These words are a great way of dealing with a consonant-heavy round of Bananagrams. Check them out:

• cwm (pronounced /koom/) - a Welsh word meaning circular or bowl-like valley, often formed by a glacier.
• crwth (/krooth/) - an archaic Welsh stringed instrument - like a boxy violin (Parenthetically, writing this definition has inspired me to make up my own (suboptimal) pangram: The King of Quips seized the crwth (like a boxy violin) to jam.)

Another one is bwlch which means mountain-pass, and is kind of fun to say. "I pity the /boolch/!".

Some other good words for getting rid of consonants:

• hymns
• fjords
• rhythms
• strengths (the longest dictionary word with only one vowel)

The other option when you have too many consonants is, of course, to dump one of them, in hopes of getting some vowels. There are 63 vowels in a Bananagrams set (counting Y as a vowel), so if you pick 3 tiles from a random pool (starting with all 144 tiles), the probability of getting all consonants would be 81/144*80/143*79/142 which is about 18%. (The probability of getting all vowels is 8%.) [The odds could be computed more efficiently if you took into account all the tiles already turned over. This could be useful near the end of the game, but would seem to require superhuman ability to catalog all the displayed tiles. It seems more plausible in the final move of a Scrabble game.]

So, about 80% of the time you'd probably come out ahead (with one or more extra vowels) though possibly with much rearranging to do to use your new tiles. The other 20% of the time you'd just have more consonants and be even more stuck! This is one reason that I generally only dump at the beginning of a game or else when absolutely necessary.

Letter distributions in Bananagrams and other games

What determines how many of each letter there are in various word games? The inventor of Scrabble designed the frequency of his tiles around the frequency of letters used on the front page of the New York Times. (Somebody must have sat and done a lot of counting back in 1938.) The distribution for Snatch is said to be based on the frequency distribution of letters in the English language as calculated by World War II cryptographers.

This photograph visually displays the letter distribution for Bananagrams. (Click for a larger version.)
The following table gives the letter distributions for Bananagrams, Scrabble (without the blanks), and Snatch:

Game	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
Bananag.	13	3	3	6	18	3	4	3	12	2	2	5	3	8	11	3	2	9	6	9	6	3	3	2	3	2
Scrabble	9	2	2	4	12	2	3	2	9	1	1	4	2	6	8	2	1	6	4	6	4	2	2	1	2	1
Snatch	5	2	4	4	12	4	2	5	5	1	1	5	4	5	6	3	1	5	5	7	4	2	3	1	3	1

By comparing the Bananagrams and Scrabble sets, we learn that the Bananagrams set of tiles is a superset of the Scrabble set of tiles (except for the blanks). In fact, for each letter of the alphabet, the Bananagrams set has at least one more tile than the Scrabble set. Since there are 100 Scrabble tiles and 144 Bananagrams tiles, this additional 26 tiles explains a lot of the discrepancy. It also gives a hint as to how the inventors of Bananagrams may have derived their distribution.


The Snatch set, on the other hand, is NOT a subset of the Bananagrams set. If you want to try to play Snatch with a Bananagrams set of tiles (and if you are kind of a stickler), you can get close to the right distribution by throwing out these letters in these numbers: (A,7), (E,5), (I,6), (O,4), (R,3). (I am reducing each difference by one to allow for a slightly larger Bananasnatch set (121 tiles instead of 100).) You can remember this with the mnemonic lAttIcEwORk and noting that you start by throwing out 7 tiles lettered A, decreasing the number by one for each of the vowels, and finally setting aside 3 tiles with the letter R on them.

UPDATE:
I found the letter distribution for Spanish Bananagrams here and the French Bananagrams letter distribution here.

Here is the revised table, in vertical format (to accommodate the extra letters):

	B a n a n a g r a m s	S p a n i s h B G	F r e n c h B G	S c r a b b l e	S n a t c h
A	13	17	13	9	5
B	3	3	3	2	2
C	3	5	4	2	4
D	6	7	6	4	4
E	18	17	18	12	12
F	3	2	3	2	4
G	4	3	2	3	2
H	3	3	2	2	5
I	12	8	12	9	5
J	2	2	2	1	1
K	2	1	1	1	1
L	5	5	6	4	5
M	3	3	4	2	4
N	8	7	9	6	5
O	11	12	12	8	6
P	3	3	4	2	3
Q	2	2	2	1	1
R	9	7	10	6	5
S	6	8	6	4	5
T	9	6	10	6	7
U	6	7	6	4	4
V	3	2	4	2	2
W	3	1	1	2	3
X	2	1	2	1	1
Y	3	2	1	2	3
Z	2	2	1	1	1
CH		2
LL		2
Ñ		2
RR		2

---

Suggested reading:

• The Boggle cube redesign and its effect on the difficulty of Boggle
• The longest word that you can make in Bananagrams

The game of Snatch (a.k.a., Anagrams)

I recently learned a great game that can be played with the Bananagrams tiles. It is currently sold under the name "Snatch", but earlier versions actually pre-date Scrabble and, if the Wikipedia entry can be believed, has existed in some form since the Victorian era.

Like Bananagrams, it can be played with 2 to many players, but also like Bananagrams, it seems like (tentatively) 4 is the optimum number.

The object is simply to build words from the available tiles. Start with all the letters face down in the center of the table. One player starts turning over tiles until someone sees a combination of tiles that make a word (at least 3 letters long). They shout out the word and claim it. Then the next player starts turning over tiles. What makes the game interesting is that, even a word that have been claimed by a player can be snatched away if someone sees a way to combine all of its letters with one or more tiles from somewhere else on the table to make a new word. New words must have a different meaning. (You can't just use another form of the word. For instance, if someone has the word TONE, the variations TONES and TONED are not allowed. STONE, on the other hand, would be a legitimate snatch.) You can build off of your own words, and you can combine the letters from multiple words to form a single new one.

The rule that I really like is that, if you see a word, you can snatch it at any time. For example, Alice turns over a tile. Bob sees a word and snatches it. Your first reaction (from the paucity of options when the game first starts), is to wait for Bob to take his turn flipping tiles. But if you see a word, you can grab it immediately.

Ties: If Alice and Bob both call out words at the same time and the words share at least one tile, the conflict can be resolved by yielding to whoever has the longer word. You should make up your own house rule for when two players call out the same word (or words of equal length) at the same time. (One idea is to throw those tiles back into the pool.)

When all the tiles have been turned over, play continues until everyone decides that there are no more moves to make and quits. Scoring is completely arbitrary. I like counting the number of words, but admittedly, this penalizes for combining two of your own words to form one longer one.

You can play Snatch with Bananagrams tiles (which I call "Bananasnatch"), but you may find that there are a few too many vowels as the Bananagrams set is optimized for Bananagrams while the Snatch set is designed for playing Set. I threw out about 12 of the vowels and found that we had a pretty good game. Throwing out more may make the game steadily more challenging. I will have a more detailed analysis of the letter distributions in a forthcoming post.

After playing one round of Bananasnatch, everyone wanted to play again. It is tremendous fun! It's perfect for when you've played six or seven rounds of Bananagrams and you want to change things up a little bit.

Appletters & Pairs in Pears: New games from the makers of Bananagrams

I stumbled onto this blog entry, describing a bit of the Bananagrams origin story, and then revealing that the Bananagrams people are about to release two new games!

So far, I've only found out that Pairs in Pears has tiles that augment the letters with patterns (dots, lines, blank and solid), and that it is aimed at kids, helping them to work on "cognitive skills and memory, as well as the order of the alphabet, vocabulary and rhyming as they practice forming words".

And I can find no information at all about Appletters. Not even how to pronounce its name. Just that it exists. Here is a fuzzy picture of Appletters:

If you have any information about the nature or current whereabouts of either of these games, please send it in to our anonymous hotline.

UPDATE: I have obtained what appears to be an official description of Appletters: "A fun domino game... You don't connect the dots -- you connect the letters!"

UPDATE^2.1: I've posted new information about Appletters here and Pairs in Pears there.

Bananagrams online tournaments announced

According to the Bananagrams Twitter feed, there will be a tournament for the online version of Bananagrams (i.e., through Facebook and possibly other sites) on Monday, July 6th, 2009.

The event is described here (Facebook login required, but here is the relevant text) :

This is it, folks...the moment you've been waiting for.

You all have been practicing, so now it's time to show your stuff! The Bananagrams "Happy Monday" contest is a way for YOU, the players, to earn prizes and gain fame!

Here are the rules: Beat as many players as you can in Live Multiplayer games on Monday, July 6th, from 12:00am-5:00pm. That's it. Simple, right?

* GRAND PRIZE: 5,000 free Benjees and a set of elite TROPHY TILES (not available in the store).

* 2nd place: 2,500 free Benjees and 10 Charms.

* 3rd place: 1,000 free Benjees and 5 charms

* All top 25 players receive 250 Benjees and 3 charms.


The excitement begins on Monday, so start practicing and get ready to win! GOOD LUCK!

It's a virtual game, so all the prizes are virtual, too. I'm guessing that the "Benjee" is the online Bananagrams unit of currency for buying things in the virtual Bananagrams store. I do like the look of those trophy tiles!

UPDATE: This has turned into a regular, weekly event.

LATER UPDATE: These online tournaments have ceased, but I'm leaving this up for historical purposes.